Год выпуска: 2012 Автор: Angela Mestre Издательство: LAP Lambert Academic Publishing Страниц: 112 ISBN: 9783659131738
Описание
In perturbative quantum field theory, the n-point functions consist, in general, of an infinity of Feynman graphs. Traditionally, these are generated via functional methods. This book describes the relation between complete, connected, and 1-particle irreducible n-point functions directly at the level of the Hopf algebra of time-ordered field operators. The ensembles of time-ordered n-point functions are simply linear forms on this algebra. It is showed, for instance, that the complete and connected n-point functions are elegantly related through the convolution product (induced by the coproduct). In this setting, a simple algebraic relation between connected and 1-particle irreducible n-point functions is derived, while the connected n-point functions are expressed in terms of their loop order contributions. At the center of the work stands a Hopf algebraic representation of graphs and a new algorithm to recursively generate all trees or all connected graphs and their values...
